It's entirely possible, cheap, and simple. Go to the main bus terminal in Puerto Iguazu. Get on a bus going to Cuidad de Este (it'll likely just say 'Paraguay'), and it travels across into Brazil to Foz Iguacu, and then across another bridge into Cuidad de Este.
You'll go through customs/border at Argentina/Brazil, and then...probably again going into Paraguay. Talk to the bus driver, at this point it gets a little sketchy, but...yeah, sometimes they just skip the border.
From my blog post on doing exactly this trip:
Let’s just say hypothetically there’s this bus, and there’s this
hypothetical driver, who upon hearing that the only non-local on the
bus only wants to go into the border town, can’t be bothered getting
the tourist a stamp, drives on through the express customs lane for
locals, and says he can just do the same on the way back after picking
the tourist up again. Imagine that. Hypothetically of course.
Hypothetically said tourist would hypothetically be in Paraguay
without a visa and without a stamp, wandering around Cuidad de Este.
But yes, there is a bus, and it does take you via Cuidad de Este - and indeed it continues all the way to Asuncion if you really wanted to go that far. It's very easy, and all it really requires is you getting on the bus. But do make sure that you have a visa for Paraguay, and check whether you need one for Brazil as well.